For convenience, we have focused on the HP model with its minimal two-letter alphabet. To extend the approach
to models with larger alphabets, such as the 20-letter Miyazawa-Jernigan model [1]}, is straightforward,
as it amounts to simply changing the interaction parameters in Eq. REF .
Moreover, although the checkerboard division into even and odd sites may have to be modified or abandoned,
the method can be applied to an arbitrary graph. In particular, it can be directly applied to
three-dimensional grids, including the tetrahedral one used in Ref. [2]}.
